This invention relates to the mathematical analysis and manipulation of ordered information, such as color, specifically for the mapping of complex color effects onto images encoded using fractal geometry and computer graphic image technology. More specifically, this invention relates to improvements whereby natural features of an image of a real two-dimensional or three-dimensional objects may be preserved while controlling the colorization of the image, either from gray-scale images to color or from colors of one palette to colors of another palette.
This invention derives elements from the fields of color science, fractal geometry and information visualization in computer graphics. Various systems have been used to represent colors. Computers usually represent color by the amount of red, green and blue components, and printing uses the four component cyan, yellow, magenta and black. Human color vision is based on a system of primary receptors for red, yellow and blue.
The first standardization of the specification and quantitative classification of color and the differences between color occurred in 1931. The Commission Internationale d'Elairage (CIE-The International Commission on Illumination) picked the lighting standards under which color would be measured and classified. A filter was used which produced a spectrum very close to daylight when illuminated with a tungsten lamp at the proper temperature, this became known as Illuminant Standard C. A second standard called Illuminant Standard A was adopted which has a similar energy distribution to a gas-filled tungsten lamp.
The measurement of color was standardized using a tri-stimulus system. X represents the spectral color red at 600 nm, and X represents a standard more saturated than X. Y and Y represent a more saturated standard and spectral green respectively at 520 nm, and Z and Z represent a more saturated standard and spectral blue at 477 nm. Any color can be represented thereby by integrating over the region of the spectrum which represent the peaks for the red, green and blue standards. The calculations are lengthy and computerized spectrophotometers and photoelectric cells are commonly used. The color standards were chosen so that the green standard matched exactly the reading for that wavelength on a curve of luminosity/unit of power as a function of wavelength. In this way the luminance of colors can be related to the luminance of pure white or black.
Because color is represented, measured and quantified using color space, graphical methods are useful for visualizing aspects of color space. Because color space is a three-dimensional entity, it is difficult to represent graphically in two dimensions. For this reason, a two-dimensional system was developed called the chromaticity diagram. The red component of a color described using the tri-stimulus system is given by the formula x=X/(X+Y+Z). The green component is y=Y/(X+Y+Z) and blue is z=Z/(X+Y+Z). Because x+y+z=1, only two of these quantities are independent and color can be represented by graphing two of the above quantities. Colors can be plotted on the x-y, x-z and y-z planes. The y-x plane is normally used for the chromaticity diagram.
The chromaticity diagram allows additive color mixture to be accomplished graphically. This cannot be done using the RGB tri-stimulus coordinates of two colors. The chromaticity diagram has a serious limitation for color measurement and the visualization of relationships between colors. A chromaticity diagram is a two-dimensional projection of a three-dimensional space. It contains distortions similar to those seen in the two-dimensional Mercator projection of the earth commonly used in maps. The distances between two colors in the chromaticity diagram do not necessarily accurately reflect their actual positions in color space.
The system just described is mainly used for quantitative color specification. To represent color in a manner which is most useful in the fields of art, design, and color photography requires a system of color ordering. The attempt to order colors has a rich history. It is believed that Leonardo da Vinci was the first to attempt color ordering by painting similar colors close to one another, and different colors further away. Newton was the first to arrange the hues in a circle with complementary hues occupying opposite positions on the circle. In 1745, Moses Harris arranged colors of the same hue but increasing saturation at increasing distances from the center along the radius of a circle.
Ostwald in the early 1900s distributed grays between black and white along an axis perpendicular to the circle of hues. Ostwald used a double cone for color space, a system that did not accurately reflect the quantitative relationships. The Ostwald system was the first to order color as a function of all three descriptive variables. These are most commonly called hue, saturation and value. Hue is the actual color such as red, green or blue. Saturation is the amount of the color. Colors with very low saturation are almost on the gray scale. Value is the same as brightness. Value orders colors with hue along the gray scale from black with zero value to white with a maximum value.
The double cone of the Ostwald system is not a true representation of color space. Each hue can vary in both brightness and saturation. The true space of hue, saturation, and value (brightness) is a cylinder. At the same time that Ostwald developed his color ordering system, the artist Munsell prepared a series of cards which represented the saturation and value or brightness of different hues. He developed cards for ten hues, ten value gradations and three to eight saturation steps for each view. These cards have been commercially available since 1904. The Munsell system has been very useful for artists and designers because it provides a logical and correct ordering of colors.
A technical analysis of color shows that hue corresponds to spectral frequency range, brightness corresponds to amplitude (as a function of frequency) and saturation corresponds to signal-to-noise ratio (as a function of frequency).
The Optical Society of America has evaluated the color order systems and used human observers to develop uniform color scales representing the color continuity and metric. A standardized set of scales was adopted in 1974. The optical society decided to adopt a set of 500 colors in Munsell color space that allowed arrangement into the maximum number of scales. A committee was employed to locate 500 points of equal perceptual distance in the three-dimensional color space based on the Munsell system. The lattice of points was arranged and depicted as colored spheres in a regular rhombohedral crystal. Each point in the lattice is equidistant from twelve other points. A three-dimensional model of this space was built using colored balls. This model contains 422 uniform scales of three or more steps.
The beauty of color use in art is based on the use of such color scales where colors are changed in graded steps. The model constructed by the optical society represents the current state of the art in the visualization of color scales. However, most books on color for artists and designers are restricted to a few major color scales. Tint scales add increasing amount of the achromatic color white to pure hues. Shade scales add increasing amount of achromatic black to pure hues. Tone scales add increasing amounts of colors on the gray scale. There are also "uniform chroma" scales which are tint, tone, or shade scales with compensating amounts of pure hue added to keep saturation constant.
The physical representation of color scales by the Optical Society of America is by no means complete. The lack of completeness has been underscored by the development of twenty-four-bit computer graphic systems which have made palettes of 16.8 million colors available for use. This is a much wider range of color choice than has ever been available to an artist. There have been no tools which enable the visual artist to take full advantage of this color capability. Even the best twenty-four-bit computer painting programs lack techniques which allow color use in computer graphics to come close to the remarkable display of colors in nature. This is one of the starting points for the present invention. What is needed is a systematic tool for utilizing the full color possibilities of twenty-four-bit graphics.
This invention also relates to the visualization of information. The process of map making has been expanded to such maps as maps of galaxy distribution, maps of brain activity, maps of genes on the human genome, and satellite maps of the earth and ocean surfaces. In addition, there is increasingly sophisticated medical imaging and visualization in complex data bases. Many maps use color to reveal pattern. Heretofore, color choice has been arbitrary and without a systematic method of choosing and scaling colors that best highlight the patterns.
The parent invention was particularly useful to fractal geometry, a geometry of fractional dimensions which describes objects or sets via the procedures which generate them. There is a branch of fractal geometry useful for image compression of real-world images. One interactive method, Barnsley, U.S. Pat. No. 4,941,193, sometimes requires the mapping of colors onto a fractally-encoded image. Therein the colors are mapped onto numerical measures which are generated by the fractal mathematics. Alternatives for color imaging may provide advantages over the Barnsley technique used for color mapping.
While the invention disclosed in the parent application provides systematic tools for choosing appropriate palettes for various maps and for scaling the color transitions to best highlight desired features, the techniques disclosed therein were best adapted to irregular geometric patterns which already had an inherent order, such as fractal maps. However, only limited control was provided to retain natural features of contrast exhibited primarily as luminance (value), as found in images of natural objects, such as three-dimensional objects or two-dimensional decorative patterns with high color symmetry related to shape. What is needed is a mechanism allowing the recoloring of images while retaining key aspects of contrast which carry geometric information.